Maeve Stern, of Westfield, was among the protestors at the State House on May 16 who were visiting legislators to reinvest in public education.Craig F. Walker/Globe Staff/Globe Staff

Towns are threatening lawsuits. Teachers, students, and other activists thronged the State House and the Boston Common demanding more money for schools. Officials in struggling urban districts say they’re counting on the Legislature to deliver a revamped funding formula by the time they start the next school year.

Amid this external pressure, the House and Senate chairs of the Legislature’s Education Committee say they hope to unveil as soon as next month a consensus bill to overhaul Massachusetts’s troubled education funding formula, which a legislative commission concluded nearly four years ago is shortchanging K-12 education in the state by $1 billion or more.

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The education bill has emerged as the most high-profile piece of legislation on Beacon Hill so far this session, the sole policy priority that leaders across both chambers and the governor’s office agree they want to complete this year.

But pitfalls remain. The Legislature’s gears move slowly, and various players have drawn lines in the policy sands that could be hard to bridge. House Speaker Robert DeLeo provided a glimpse of the political tensions involved when he issued a statement accusing the Massachusetts Teachers Association of engaging in “juvenile tactics” during a May 16 rally, after the union’s president posted a picture of herself and other women clutching at strings of fake pearls around their necks. “Alice Peisch, let go of the wealth and #FundOurFuture,” the caption read. Representative Peisch is known to wear pearls.

“Now is the time to dig into the details of this nuanced, complicated formula — not for stunts,” DeLeo said in a statement, after praising Peisch for “tirelessly working” on the legislation.

In 1993, the Legislature passed the landmark Education Reform Act, creating what’s known as the foundation budget, a formula that attempts to predict the minimum cost for each district to educate its students and how much state aid each community should get toward that budget.

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The formula was supposed to be updated regularly, but lawmakers demurred and in the years since, it has failed to keep pace with inflation, forcing communities to pay more for health insurance and special education, among other programs, and creating stark disparities across the state.

Reflecting the sense of urgency the education issue has taken on, the House and Senate chairmen of the Joint Education Committee are trying to hammer out a bill to overhaul the 26-year-old formula.

Peisch and Senator Jason Lewis of Winchester have been meeting regularly. They’ve solicited input from teachers, parents, and other advocates and specialists, and they have traveled to school districts across the state as they wrestle with the policy details that contributed to the Legislature’s failure to reach an agreement on a funding formula bill last session. Much of their work has focused on how to ensure districts with high numbers of low-income students have the resources they need.

The goal, said Lewis, is to unveil a bill by next month and have the full Education Committee vote in support of it.

“I’m optimistic the bill will have broad support,” he said.

“We’re making good progress, and I’m hopeful that we will be able to report something out of the committee soon,” said Peisch.

She was less willing to commit to a specific timetable but called Lewis’s target of sometime in June “within the realm of possibility.”

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The bill would still have to go through debate and votes in each separate chamber; any resulting differences would need to be reconciled. But the chairmen seem focused on resolving many of the major issues now, to avoid grappling with them in 11th-hour conference negotiations.

Last session, the state House and Senate passed differing bills to retool the funding formula, but negotiations collapsed without a deal at the end of the session.

“We are purposely making this issue a high priority early in the legislative session so we’ll have plenty of time to resolve any remaining differences,” said Lewis.

A major unresolved area in their effort is figuring out how much more money to pump into districts that educate high numbers of low-income students. These are the places where often students have fallen the furthest behind achievement levels seen in wealthier districts.

The state’s funding formula gives districts a chunk of money on top of the base line per-pupil budget for educating low-income students, a recognition that they need more resources.

The issue of how much to boost the low-income student allocation is a potential fault line in the coming debate. Many advocates insist any legislation needs to double the amount of extra money spent on low-income students, which is what has been proposed in a bill known as the Promise Act.

Under current law, the highest poverty districts such as Brockton and Worcester receive an additional $3,980 for each low-income student. The Promise Act would boost that supplement to an additional $7,910 for each low-income student, according to Steve Crawford, a spokesman for Fund Our Future, a coalition composed of the Massachusetts Teachers Association, the American Federation of Teachers Massachusetts, and more than three dozen other unions, civil rights advocates, and parent and student organizations.

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Legislation introduced by Representative Paul Tucker would require an increase in per-pupil funding for low-income students of at least 50 percent for districts serving fewer low-income students. That figure would increase by an amount to be determined by the Legislature in districts serving higher concentrations of low-income students.

Advocates do not think that is enough to close the achievement gap, said Crawford.

Senator Sonia Chang-Díaz of Jamaica Plain, the lead champion of the Promise Act, said whatever bill comes out of the Education Committee must implement all the recommendations made by the 2015 commission, “including and especially the full low-income rate.”

Another potential sticking point: What extent lawmakers seek to tie new money to new benchmarks or other measures. Teachers unions and others don’t want to see onerous new conditions placed on state aid. “Local teachers know what their kids need the most, not state education bureaucrats,” said Crawford, of the Fund Our Future coalition, which organized the major demonstration on Beacon Hill and the Boston Common earlier this month.

Governor Charlie Baker, however, has been pushing for legislators to include measures to ensure the new infusion of money goes to help students at struggling schools.

It’s a view echoed by business groups and other players, including some officials in cash-strapped school districts.

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At a recent event, Baker listed his key priorities for the bill, including a new $50 million “school improvement” fund, money the commissioner of the Department of Elementary and Secondary Education can give to troubled schools to fund specific performance-boosting initiatives, such as after-school programs or longer school days.

“There are always plenty of people in the building who will advocate for money. That one usually has a fairly big crowd,” Baker told members of Boston Leaders for Education at a May 14 breakfast. “Advocating for kids, especially for kids in districts where we need to do better, and especially advocating for different and new ways to think about how to deliver — that’s a different kind of conversation,” he said, asking the group’s members to reach out to lawmakers.

CORRECTION: An earlier version of this story mischaracterized Representative Paul Tucker’s education funding proposal. It would require an increase in per-pupil funding for low-income students of at least 50 percent for districts serving fewer low-income students. That figure would increase by an amount to be determined by the Legislature in districts serving higher concentrations of low-income students. Additionally, the Promise Act has support in both the Senate and House.